Many computer graphics applications, including computer games and 3-D animated films, make heavy use of animated meshes, also known as deforming mesh sequences. Designing and producing visually pleasing mesh sequences, either manually or through physically-based simulation, is a costly and time-consuming process, during which effects caused by interactions between the deforming object and its surroundings need to be considered. For example, a running horse needs to adjust its pace and body configuration according to obstacles and turns in the path as well as undulations on the terrain. This motivates a methodology to automatically create novel mesh sequences by reusing and adapting existing ones.
The goal of adapting existing deforming mesh sequences is to conveniently produce desired sequences that satisfy requirements from both the user and the environment. Compared with static meshes, deforming mesh sequences have an additional temporal dimension that leads to greater data complexity and a few new technical challenges. First, a paramount demand is minimizing the amount of user intervention. This is especially important for long sequences and dictates whether the entire editing system is truly usable.
Second, with minimal user intervention, the system should still permit both flexible and precise user control. Third, given very sparse constraints, the system should be able to produce desired results that preserve both temporal coherence and important characteristics of the deformations in the original mesh sequence.
Laplacian mesh editing extracts intrinsic geometric properties, such as differential coordinates, from the original mesh, subjects them to local transformations during editing, and finally reconstructs new meshes from the transformed differential coordinates by solving a global system of equations. The reconstruction step makes local editing in differential coordinates have a global effect on the new mesh.
The composition of these steps leads to an overall nonlinear process. Due to the existence of efficient solvers for sparse linear systems, much effort has been devoted in the past few years to obtaining approximate solutions using either linearizations or multiple linear passes. The latter typically requires explicit rotational constraints. Alternatively, the problem can be cast as a nonlinear optimization without rotational constraints. Since nonlinear optimizations require more expensive iterative steps, subspace methods have been developed to achieve acceleration. Laplacian mesh editing, however, has not been previously generalized to the spacetime domain.